Open AccessThe effect of numerical integration in mixed finite element approximation in the simulation of miscible displacement
Author(s) -
Pongui Ngoma Diogène Vianney,
Germain Nguimbi,
Likibi Pellat Rhoss Beaunheur
Publication year - 2017
Publication title -
international journal of applied mathematical research
Language(s) - English
Resource type - Journals
ISSN - 2227-4324
DOI - 10.14419/ijamr.v6i2.7320
Subject(s) - mathematics , finite element method , displacement (psychology) , mathematical analysis , thermodynamics , physics , psychology , psychotherapist
We consider the effect of numerical integration in finite element procedures applied to a nonlinear system of two coupled partial differential equations describing the miscible displacement of one incompressible fluid by another in a porous meduim. We consider the use of the numerical quadrature scheme for approximating the pressure and velocity by a mixed method using Raviart - Thomas space of index and the concentration by a standard Galerkin method. We also give some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal order estimates are derived when the imposed external flows are smoothly distributed.